Topological complexities of finite digital images

Abstract

‎Digital topological methods are often used in computing the topological complexity of digital images‎. ‎We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a digitally connected finite digital image‎. ‎We present all possible cases of the topological complexity TC of a finite digital image in $\mathbb{Z}$ and $\mathbb{Z}^{2}$‎. ‎Finally‎, ‎we determine the higher topological complexity TC$_{n}$ of finite irreducible digital images independently of the number of points for $n > 1$‎.